A Flexible Moderated Factor Analysis Approach to Test For Measurement Invariance Across a Continuous Variable

Effort has been devoted to the development of moderated factor models in which the traditional factor model parameters are allowed to differ across a moderator variable. These models are valuable as they enable tests on measurement invariance across a continuous background variable. However, moderated factor models require the specification of a parametric functional form between the factor model parameters and the moderator variable while, in some situations, it is unclear what functional form to assume. Therefore, in the present article, a semiparametric moderated factor modeling approach is presented in which no assumption concerning the functional form between the moderator and the model parameters is imposed. In a simulation study, the semiparametric moderated factor model is shown to be viable in terms of parameter recovery and the power to distinguish the different models for measurement invariance. In addition, the model is applied to a real dataset pertaining to intelligence.